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. 2014 May;104(5):507-513.
doi: 10.1257/aer.104.5.507.

Rational Attention and Adaptive Coding: A Puzzle and a Solution

Camillo Padoa-Schioppa  1 , Aldo Rustichini  2
Affiliations

Rational Attention and Adaptive Coding: A Puzzle and a Solution

Camillo Padoa-Schioppa et al. Am Econ Rev. 2014 May.
No abstract available

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Figures

Figure 1
Figure 1
Challenge Posed by Range Adaptation Notes: Panel A: Range adaptation in orbitofrontal cortex. Each line represents the average neuronal response (baseline-subtracted) plotted against the offer value. Different lines indicate different value ranges. Panel B: In this simplified model, choices result from the activity of two neurons encoding offer value A (left) and offer value B (right). When the range of juice B increases (lighter line), the offer value B cell adapts. The indifference point, for which the two cells have equal firing rate, shifts. If decisions were made by comparing firing rates, the same quantity of juice B would be chosen less frequently. Source: Panel A reproduced from Padoa-Schioppa (2009)
Figure 2
Figure 2
Dynamics of Gating Variables and Choice Process (Axes indicate the variables S) Notes: Arrows describe the direction of flow of the differential equation (2) and its correspondent for the B good, when the input I i (t) is constant over time for both goods. The two lines describe the zeros of the vector field; their intersection the steady states, thus the possible limit values of the two gating variables. Two of the steady states are stable and one (the intermediate) unstable. In panel A, the input for the two goods is the same, so with noise the two goods are chosen with equal probability. In panel B, the input of good A is higher; the set of zeroes for the S A variables shifts upward. Now a process starting at the initial condition S i = 0 for both goods is more likely to converge to the bottom-right steady state. So the probability of choosing A is higher than 1/2. With a further increase of the input for A, only one steady state will remain, and good A will be chosen for sure.
Figure 3
Figure 3
Dynamics of Hebbian Learning (Axes indicate the weights) Notes: Arrows describe the direction of flow of the ordinary differential equation (7), and the corresponding equation for good B. The environments are uniform distributions. The two lines describe the zeros of the vector fields; their intersection the steady state, thus the limit values of the two weights. In panel A, the ranges of offers of the two goods are the same, and the two steady states have equal value. In panel B the range of good A is doubled in size, that of good B is unchanged.
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